I am observing the fluxes of source and I am trying to learn something from it's distribution of fluxes.
When I histogram my data, I can perfectly describe my data with a lognormal distribution. That was in fact what I had expected, but I was still curious if I could find other description for the flux distribution.
From a physical model point of few, a scenario where the fluxes are distributed according to the gamma distribution would make sense (for which I have a mind-picture of "events for which a waiting time is relevant").
To my disappointment the Gamma Distribution did a very poor job in describing the data. In a trail and error approach, I went forth and fitted the flux distribution with the Inverse Gamma Distribution. I found it to be a perfect fit for my data, even better than LogNormal distribution (not significantly in a chi^2 sense though).
I am now a bit dumb-struck:
First, because I don't have a "mind picture" for the inverse gamma distribution. Does it ever occur in nature other than being a vehicle for Bayesian interference? Could you provide such a "mind picture"?
Second, is there any reason for the Inverse Gamma distribution to fit some exponential data, other than it being a "flexible function" (flexible in a sense that I could probably fit a polynomial of some order to may data as well).